What to do when Pesach occurs on Saturday night

When Erev Pesach occurs on Shabbat when is
Bedikat Chametz (checking for chametz)?

Do we eat bread at all of the Shabbat Meals?

Dear Balint,

First of all, a few relevant points of Jewish Law:

This year, the Fast of the First Born is on Thursday,
March 24, 1994. It begins at dawn and ends after the Evening services.
Preferably, one should not eat until after Bedikat Chametz, but
may have a snack after the Evening prayers if hungry. Many people
attend a Siyum (a celebration of the completion of a Tractate
of the Talmud), a Brit Mila, or a Pidyon Haben on the day of the
fast, and are thereby permitted to eat afterwards.

Bedikat Chametz is done on Thursday night, immediately
following the Evening prayers. After checking for chametz, you
should take any chametz that you plan to eat on Friday and Shabbat,
and put it in a safe place where it won't be forgotten.

One should burn the chametz on Friday morning, preferably
during the fifth daylight hour (check a local Jewish calendar
for the exact time). One does not nullify ownership of the chametz
on Friday -- rather this should be done on Shabbat during the
fifth daylight hour. On Shabbat one may not eat Matzah, because
we want its taste to be fresh at the Seder -- so we must use
bread for the Shabbat night and morning meals. Because
bread may not be eaten after the end of the fourth daylight hour,
one must eat the morning meal prior to this time.

The third meal poses a problem, because there
are some Halachic authorities who state that the third meal must
be eaten in the afternoon, and there are also authorities
who rule that one must eat _bread at the third meal. It is forbidden
to eat bread after the end of the fourth daylight hour so what
do we do? The preferred scenario is as follows: You get up very
early on Shabbat morning, pray, make Kiddush, wash hands for bread,
eat Challah with a light meal, and recite Birkat Hamazon. You
then leave the table for a short while, wash again, eat bread,
and again say Birkat Hamazon. All of this must be completed by
the end of the fourth daylight hour. Later in the day you sit
down to a meal of Kosher for Passover food (meat, fruit, salads).
If the end of the fourth hour is approaching -- don't risk having
another meal of chametz. Wait until later, and eat a meal that
is Kosher for Passover.